Pure Time Delay Research Articles

Design and application of PIP controllers: robust control of the IFAC93 benchmark

Proportional-integral-plus (PIP) controllers exploit the full power of optimal state variable feedback within a nonminimum state space (NMSS) setting. They are simple to implement and provide a logical extension of conventional proportional-integral/proportional-integral-derivative (PI/PID) controllers, with additional dynamic feedback and input compensators introduced automatically when the process is of greater than first order or has appreciable pure time delays. The present paper provides a tutorial introduction to the NMSS/PIP control design methodology and associated system identification procedure. The latter is based on the utilization of the simplified refined instrumental variable (SRIV) algorithm for the estimation of transfer function models. The practical utility of these techniques is illustrated by their application to the IFAC93 benchmark system, a seventh-order stochastic simulation whose parameters vary randomly within specified ranges. This benchmark provides a good simulation example for tutorial purposes, since it requires the control engineer to work through all the usual design steps, including identification of a low-order control model, control system design, and implementation using a standard programming language, in this case ‘C’. Finally, note that the statistical estimation tools described in the paper have been assembled as a tool-box within the Matlab™ software environment.

Iterative learning control with Smith time delay compensator for batch processes

How to improve the control of batch processes is not an easy task because of modeling errors and time delays. In this work, novel iterative learning control (ILC) strategies, which can fully use previous batch control information and are attached to the existing control systems to improve tracking performance through repetition, are proposed for SISO processes which have uncertainties in modeling and time delays. The dynamics of the process are represented by transfer function plus pure time delay. The stability properties of the proposed strategies for batch processes in the presence of uncertainties in modeling and/or time delays are analyzed in the frequency domain. Sufficient conditions guaranteeing convergence of tracking error are stated and proven. Simulation and experimental examples demonstrating these methods are presented.

Proportional-integral-plus (PIP) control of the ALSTOM gasifier problem

Although it is able to exploit the full power of optimal state variable feedback within a non-minimum state-space (NMSS) setting, the proportional-integral-plus (PIP) controller is simple to implement and provides a logical extension of conventional proportional-integral and proportional-integral-derivative (PI/PID) controllers, with additional dynamic feedback and input compensators introduced automatically by the NMSS formulation of the problem when the process is of greater than first order or has appreciable pure time delays. The present paper applies the PIP methodology to the ALSTOM benchmark challenge, which takes the form of a highly coupled multi-variable linear model, representing the gasifier system of an integrated gasification combined cycle (IGCC) power plant. In particular, a straightforwardly tuned discrete-time PIP control system based on a reduced-order backward-shift model of the gasifier is found to yield good control of the benchmark, meeting most of the specified performance requirements at three different operating points.

USE OF B-SPLINES TO OBTAIN ACCURATE TRANSIENT RESPONSES FOR FEEDBACK CONTROL SYSTEMS WITH TIME DELAYS*

This paper is concerned with representing the transient time response of a closed-loop control system having pure and/or distributed time delays in terms of B-spline series. More precisely, it regards to the inversion of Laplace transforms of irrational type with the B-spline series expansion approach. The B-spline series for a time function/(f) with r ≥ 0 contains first several terms in boundary splines and the remaining terms in interior B-splines. It is shown that by matching the initial conditions of the response exactly, the coefficients associated with the interior B-splines can be accurately obtained by a computationally efficient FFT-based algorithm.

Force and surface mechanomyogram frequency responses in cat gastrocnemius

Muscle surface displacement is a mechanical event taking place simultaneously with the tension generation at the tendon. The two phenomena can be studied by the surface mechanomyogram signal (MMG) (produced by a laser distance sensor) and the force signal (from a load cell). The aim of this paper was to provide data on the reliability of the laser detected MMG in muscle mechanics research. To this purpose it was verified if the laser detected MMG was suitable to estimate a frequency response in the cat medial gastrocnemius and its frequency response was compared with the one retrieved by the force signal at the tendon level. The force and MMG from the exposed medial gastrocnemius of four cats were analysed. The frequency response was investigated by sinusoidally changing the number of orderly recruited motor units, in different trials, in the 0.4–6 Hz range. It resulted that it was possible to model the force and MMG frequency response by a critically damped second-order system with two real double poles and a pure time delay. On the average, the poles were at 1.83 Hz (with 22.6 ms delay) and at 2.75 Hz (with 38 ms delay) for force and MMG, respectively. It can be concluded that MMG appears to be a reliable tool to investigate the muscle frequency response during stimulated isometric contraction. Even though not statistically significant, the differences in the second-order system parameters suggest that different components of the muscle mechanical model may specifically affect the force or MMG.

A real-time estimation approach to time-varying time delay and parameters of NARX processes

This paper presents a solution to the joint time-varying time delay and parameter estimation of NARX (nonlinear autoregressive with exogenous inputs) processes, where only pure time delay in input signal is considered. A modified strong tracking filter (MSTF) is proposed, and is adopted as an adaptive estimation algorithm. Three kinds of specific NARX processes are considered. The first is also the simplest, the output signal is the input with time delay plus disturbance; The second one is a simple NARX process plus disturbance; The third NARX process even has unknown time-varying parameters. For each of the NARX processes, we set up a specific estimation model, with these models the proposed MSTF algorithm can be applied to the real-time time delay and parameter estimation of the above three NARX processes. Computer simulation results demonstrate the effectiveness of the proposed approach. Moreover the robustness of the proposed algorithm against some model/process parameter mismatches is also tested via computer simulations.

Modeling of Mechanical Systems Using Rigid Bodies and Transmission Line Joints

Dynamic simulation of systems, where the differential equations of the system are solved numerically, is a very important tool for analysis of the detailed behavior of a system. The main problem when dealing with large complex systems is that most simulation packages rely on centralized integration algorithms. For large scale systems, however, it is an advantage if the system can be partitioned in such a way that the parts can be evaluated with only a minimum of interaction. Using transmission line models, with distributed parameters, physically motivated pure time delays are introduced in the communication between components. These models can be used to represent both lines in a hydraulic system and springs in mechanical systems. As a result, components and subsystems can be simulated more independently of each other. In this paper it is shown how flexible joints based on transmission line modeling (TLM) with distributed parameters can be used to simplify modeling of large mechanical link systems interconnected with other physical domains. Furthermore, it provides a straightforward formulation for parallel processing.

An interactive parameter space method for robust performance in mixed sensitivity problems

This paper presents an interactive graphical method to determine the set of fixed-order stabilizing controllers achieving robust performance, in the mixed sensitivity framework. The method is limited to single-input/single-output (SISO) systems but offers significant advantages over traditional loop gain shaping methods such as H/sup /spl infin// and /spl mu/-synthesis. It can handle pure time delays in an exact manner and the weighting functions need not be rational. The technique translates frequency-domain weighting functions and stability constraints into the parameter space and thus gives the user more insights into the design than conventional methods. By virtue of producing the required parameter space region for the frequency response criteria, subsequent optimization of secondary objectives is possible. The controllers obtained are of lower order for comparable performance than those produced by current H/sup /spl infin// and /spl mu/-synthesis techniques. The method is particularly well-suited to robust control problems where frequency-domain constraints emerge from the analysis of nonparametric uncertainties in the system and also to control problems where the frequency domain loop shaping is used to achieve time-domain specifications.

The L/sup 2/-optimal time-delay rational Laplace model revisited

An optimization technique is provided for the approximation of the pure time delay. Owing to a near-optimal starting point, the integral square error is reduced through a few iterations of a Gauss-Newton process. Compact implementation and robustness should encourage a large use in various engineering domains.

Quadratic Optimal Control through Spectral and Coprime Factorisation

We study the infinite horizon quadratic cost minimisation problem for a linear time-invariant distributed parameter system with finitely many inputs and outputs. We work in an input/output framework, and reduce the unstable case to the stable case by the use of a right coprime factorisation of the impulse response and a preliminary stabilising feedback. The stable case is then solved through spectral factorisation. The theory is illustrated with two examples involving pure time delays.

Design and Control of a Novel 3-DOF Flexible Robot, Part 2

This paper aims to present the design of a practical controller for a flexible, industrially competent, robot arm. The language used is that of a practicing control engineer, with emphasis on the physical in sights useful to the designer during the design process. This contrasts with most experimental results presented in the literature, which are usually for one- and two-link planar arms and are amenable to closed-form analysis and simulation. Such arms also manifest limited performance with respect to rigid-body manipulators, and underline the difficulties in extending controller design to more than two flexible links. Furthermore, experimenters invariably rely on the efficacy of the control algorithm, rarely exploiting their understand ing of control theory to add mechanical design features to ease the control task. The work presented in this paper centers on a three-link (spatial) flexible and industry-sized prototype arm, the Rotabot, and the purpose is to demonstrate that the control task can be simplified by using control-theory-driven mechanical design. The special de sign features of the Rotabot facilitating ease of arm dynamic control are presented in a companion paper, Part 1. The final control task, despite the care taken with the arm design, was hampered by driver nonlinearities such as torque ripple, Coulombic friction, and pure time delays within the commutation circuitry of the motors. The use of direct drive means that drive nonlinearities, which tend to have high bandwidths, are closely coupled to the vibration characteristics of the arm—a problem that tends not to arise in geared robots. These nonideal drive characteristics had to be dealt with by the controller. Simulation and experimental results are presented to demonstrate the feasibility of controlling such an arm and pave the way for a new practical research path on flexible manipulators.

Robust Digital Controller Design for MIMO Non-Linear Time-Varying Systems

A control problem in which the control task is formulated for output variables as decoupled tracking with desired output transients is stateted and solved for continuous-time non-linear time-varying MIMO systems under assumption of incomplete information about varying parameters of the system and external disturbances. A continuous-time controller based on the Dynamic Contraction Method is designed for a pseudo-continuous-time model of the control loop with a pure time delay and then Tustin transformation is used to calculate the parameters of a digital controller. In order to increase the sampling period a control law with a compensation of the time delay is used.

Frequency domain-based models of skeletal muscle

Models of skeletal muscle based on its response to sinusoidal stimulation have been in use since the late 1960s. In these methods, cyclic excitation at varying frequencies is used to determine force or muscle length amplitude and phase as functions of excitation frequency. These functions can then be approximated by models consisting of combinations of poles and zeros and pure time delays without the need to combine force–length or force–velocity relationships. The major findings of a series of frequency response studies undertaken in our laboratory revealed that: • The frequency response models for isometric force including orderly recruitment of motor units were relatively invariant of the particular strategy or oscillation level employed. A critically damped second order model with corner frequency near 2 Hz and a pure time delay best described the relationship between input stimulation and output isometric force. • The frequency response models for load-moving muscles consisted of an overall gain which is a function of mass, dependent mostly on the width of the length–force relation at a given load (force), and a frequency-dependent gain component independent of load mass. The phase lag between input and output was also independent of load. • Muscle function and architecture are the primary determinants of its isometric force frequency response. • Tendon viscoelasticity (excluding the aponeurosis) has no significant effect on isometric force dynamic response, but does have a minor effect on load-moving dynamic response. The effect of tendon in reducing or augmenting the load-moving muscle response bandwidth is muscle-dependent. • The joint produces decreased high frequency gain and uniformly increased phase lags between input excitation and output force in isometric conditions. The joint acts as a lag network in load-moving conditions, increasing the phase lag without significant effect on the gain. Despite its inherent non-linear properties, the joint does not significantly deteriorate output signal quality in either isometric or load-moving conditions. • Co-contraction strategy has a significant effect on the dynamic response of the joint. These frequency-based models have shown to be robust as long as the excitation type and mechanical conditions under which they are obtained are not varied. They are particularly useful for the design of neuroprostheses, where a dynamic description of muscle output as a function of stimulus input under given conditions is desirable.

Frequency-domain identification of gas turbine dynamics

The identification of the fuel flow to shaft speed dynamics of a twin-shaft gas turbine is addressed, with the aim of validating thermodynamic engine models. A measured input signal must be used in estimation in order to exclude the fuel feed dynamics from the model. This has been shown to present problems when fitting discrete models to engine data, and this paper examines the direct estimation of s-domain models in the frequency domain. A number of different multisine test signals were applied to the engine for the purposes of model estimation and nonlinear detection. The use of frequency-domain techniques is shown to produce high-quality models, and the tests also yield information on the levels of noise and nonlinearity and the length of the pure time delay. This work illustrates the potential of frequency-domain techniques for modeling systems where a physical interpretation is to be made of the model and where the need for accuracy requires that a measured input signal be used in estimation.

An artificial neural network-based controller for the control of induced paralysis using vecuronium bromide

This study presents an artificial neural network-based controller for regulating the level of induced paralysis during surgery using vecuronium bromide. The controller uses the myogram of a rapid muscle contractions (called twitch) to generate the appropriate infusion rate. The controller is self-adjusting and can accommodate inter- and intrapatient drug response variations. It also withstands changes in the pure time delay and nonlinear pharmacokinetic parameters of the response. Another feature of the controller is that it does not depend on a priori knowledge of the patient response model. Computer simulations using pharmacokinetic and pharmacodynamic models showed negligible steady-state error and maximum percent undershoot averaged to 6.24%. The average infusion rate for 90% paralysis was 1.22 (microg x kg(-1) x min[-1]).

Open-Loop Performance of a Fast-Response, Actively Controlled Fuel Injector Actuator

This paper describes a study of the frequency dependence of a secondary combustion process response (SCPR) produced by a gaseous fuel injector actuator that was developed for the control of unstable combustor oscillations. Initially, two different approaches are presented for determining the SCPR; one uses pressure data measured in a short combustor and the other uses direct measurements of the global combustion zone radiation in a long combustor. The results of both approaches are in good agreement and show that the fuel injector actuator produces a signie cant SCPR over a 0 ‐ 800 Hz frequency range. The results also show that the phase lag of the SCPR increases almost linearly with the frequency, suggesting that a pure time delay plays a role in the mechanisms that control the SCPR. Additional studies presented in the paper investigate the dependence of the SCPR on the characteristics of the fuel actuator and the main injector geometry. These show that the SCPR strongly depends on the location of the modulated fuel stream injection relative to the location of the primary combustion process, and that a larger SCPR is obtained when the secondary, modulated, fuel stream is injected directly into the primary combustion zone.

Interactive control system design by a mixed H/sup ∞/-parameter space method

This paper presents an interactive graphical method to determine sets of stabilizing controllers satisfying any combination of constraints on the sensitivity, complementary sensitivity, and input sensitivity transfer functions. The method is limited to single-input/single-output systems but offers significant advantages over current H/sup /spl infin// methods. It can handle pure time delays in an exact manner. The weighting functions need not be rational. By virtue of producing the required parameter space region for the frequency response criteria, subsequent direct time-domain optimization is possible. The controllers obtained are of lower order for comparable performance than those produced by current H/sup /spl infin// techniques. The method is particularly well suited to robust control problems, where frequency domain constraints emerge from the analysis of uncertainties in the system, and also to suboptimal problems, where the frequency-domain loop shaping is used to achieve time-domain specifications.

Ventilatory responses to CO 2: constant fraction vs. constant inflow administration

The purpose of this study was to determine whether the transfer function characteristics of the respiratory CO 2 control system differs according to whether the CO 2 administration method is constant fraction (CF) or constant inflow (CFlow). Ventilatory responses to CO 2 changes were measured in seven healthy subjects during random pet CO 2 perturbation by the CF and CFlow administration methods in normoxia and hyperoxia. The transfer function from P CO 2 to V̇e was estimated in the frequency domain from 0.002 to 0.02 Hz. The transfer function characteristics showed a low-pass filter character in both of CFlow and CF. The impulse responses to both the methods persisted for ≥60 sec, while the maximum amplitude (h max) of the CFlow response was statistically greater than that of the CF response in normoxic condition. The time required until the peak (t max) of the CFlow impulse response was shorter than that of CF in normoxia. Hyperoxia retarded the t max and reduced h max in both CFlow and CF, with the result that significant differences in the normoxic impulse responses were not observed between CFlow and CF in hyperoxia. To characterize the CO 2 control system quantitatively, we determined the static transfer gain, oscillatory frequency, damping factor, and pure time delay by applying a second-order delay model to the observed transfer function. The static gain was not significantly different between CFlow and CF responses in both normoxia and hyperoxia. The pure time delay and damping factor were significantly decreased for CFlow only in normoxia. We suggest that inhalation of CO 2 by CFlow modifies ventilatory response, probably mediating through the peripheral chemoreceptor activity.

Modeling of cardiovascular variability using a differential delay equation.

The influence of time delay in the baroreflex control of the heart activity is analyzed by using a simple mathematical model of the short-term pressure regulation. The mean arterial pressure in a Windkessel model is controlled by a nonlinear feedback driving a nonpulsatile model of the cardiac pump in accordance with the steady-state characteristics of the arterial baroreceptor reflex. A pure time delay is placed in the feedback branch to simulate the latent period of the baroreceptor regulation. Because of system nonlinearity model dynamics is found to be highly sensitive to time delay and changes of this parameter within a physiological range cause the model to exhibit different patterns of behavior. For low values of time delay (shorter than 0.5 s) the model remains in a steady state. When time delay is longer than 0.5 s, a Hopf bifurcation is crossed and spontaneous oscillations occur with frequencies in the high-frequency (HF) band. Further increases of time delay above 1.2s cause the oscillations to become more complex, and following the typical Feigenbaum cascade, the system becomes chaotic. In this condition heart rate, and flow show evident variability. The heart rate power spectrum exhibits a peak whose frequency moves from the HF to LF band depending on whether simulated time delay is as short as the vagal-mediated control or long as the sympathetic one.

Modelling of characteristic delays in multivariable control systems wcbsl

Pure time delays in multivariable control systems place severe restrictions on achievable feedback performance. This paper considers an approach to modelling distributed time-delay systems using discrete convolution. The basis for convolution algebra is briefly outlined and the new concepts of characteristic pattern and vector delays are introduced. A process control example is given that illustrates the concepts and shows typical results obtained using WCBSL (Windows Convolution-Based Simulation Language)